Vonk's p-adic singular moduli: extending Gross–Zagier to real quadratic fields — E8 Intelligence Research

FINDING: Vonk constructs p-adic singular moduli for real quadratic fields, extending Gross–Zagier from imaginary quadratic (CM) to real quadratic via p-adic families of modular forms. | MATH: Singular moduli j(τ) for τ imaginary quadratic; Gross–Zagier formula relates heights of Heegner points to derivatives of L-functions: L'(E,1) ~ ĥ(P)·log. Vonk's extension: real quadratic τ ↦ p-adic rigid-analytic functions on the eigencurve; uses overconvergent modular forms, Coleman's classicality, and the p-adic upper half-plane ℋ_p = ℙ¹(ℂ_p) \ ℙ¹(ℚ_p). | CONNECTION: Modular j-invariant j(τ) = q⁻¹ + 744 + 196884q + ... where 196884 = 196883 + 1 (Monstrous moonshine); j generates the field of modular functions; CM points give algebraic integers whose norms relate to class numbers. No direct 0.618/1.618 constants in the cited abstracts. | DEPTH: 8 FINDING: The core program (Gross–Zagier, 1986) computes differences of singular moduli as heights of Heegner points, linking arithmetic geometry to L-f Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com